Consider 3 equal circles of radius r, within a circle of radius r2, each to touch other two and the given circle.Statement-1 : rr2=33+1Statement-2 : incentre of triangle formed by joining centres of 3 equal circles is same as centre of given circle.

OC=r2−r r=(r2−r)cos300 ⇒r2r=23+1=2+33 =rr2=32+3

Consider 3 equal circles of radius r, within a circle of radius r2, each to touch other two and the given circle.Statement-1 : rr2=33+1Statement-2 : incentre of triangle formed by joining centres of 3 equal circles is same as centre of given circle.

OC=r2−r r=(r2−r)cos300 ⇒r2r=23+1=2+33 =rr2=32+3

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Consider 3 equal circles of radius $r,$ within a circle of radius $r_{2},$ each to touch other two and the given circle.
Statement-1 : $\frac{r}{r_{2}} = \frac{\sqrt{3}}{\sqrt{3} + 1}$
Statement-2 : incentre of triangle formed by joining centres of 3 equal circles is same as centre of given circle.

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Statement-1 is false, Statement-2 is true

Statement-1 is true, Statement-2 is false

Statement-1 is true, Statement-2 is true

answer is D.

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$O C = r_{2} - r r = (r_{2} - r) \cos 30^{0} \Rightarrow \frac{r_{2}}{r} = \frac{2}{\sqrt{3}} + 1 = \frac{2 + \sqrt{3}}{\sqrt{3}} = \frac{r}{r_{2}} = \frac{\sqrt{3}}{2 + \sqrt{3}}$

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Consider 3 equal circles of radius r, within a circle of radius r2, each to touch other two and the given circle.Statement-1 : rr2=33+1Statement-2 : incentre of triangle formed by joining centres of 3 equal circles is same as centre of given circle.

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Consider 3 equal circles of radius $r,$ within a circle of radius $r_{2},$ each to touch other two and the given circle.
Statement-1 : $\frac{r}{r_{2}} = \frac{\sqrt{3}}{\sqrt{3} + 1}$
Statement-2 : incentre of triangle formed by joining centres of 3 equal circles is same as centre of given circle.